Question

High intensity rainfall in the Higher Himalayan region causes extensive damage, because of its large droplet size. Which one of the following relationships between the kinetic energy of raindrop (E) and droplet diameter (D) explains this process?

• A. \( E \propto D^{1/2} \)
• B. \( E \propto D^2 \)
• C. \( E \propto D^3 \)
• D. \( E \propto D^4 \)

Hint:

The kinetic energy of a raindrop increases significantly with its size, as larger droplets have much greater energy and potential for causing damage during high-intensity rainfall.

Answer 1

The Correct Option is D

Step 1: Understanding the relationship between kinetic energy and droplet size.
The kinetic energy (E) of a raindrop is proportional to the mass of the droplet and the square of its velocity. Since the mass of a raindrop is proportional to the volume, and volume is proportional to \(D^3\) (where D is the diameter), the kinetic energy increases with the fourth power of the droplet diameter, \( E \propto D^4 \).

Step 2: Evaluating the options.
Option (A) is incorrect because \( E \propto D^{1/2} \) would imply a square root relationship between energy and droplet size, which is not correct.
Option (B) is incorrect because \( E \propto D^2 \) implies a quadratic relationship, which does not apply to the kinetic energy of raindrops.
Option (C) is incorrect because \( E \propto D^3 \) implies that energy increases with the cube of the droplet size, which is not the correct relationship.
Option (D) is correct because the kinetic energy of a raindrop is proportional to the fourth power of its diameter, as both mass and velocity depend on the size of the droplet.